Consecutive Integer Consecutive Integer ProblemsProblems

What is a consecutive What is a consecutive integer?integer?

Integer: natural numbers and Integer: natural numbers and zero zero

Consecutive: one after the otherConsecutive: one after the other

Ex. 1, 2, 3 or 17, 18, 19Ex. 1, 2, 3 or 17, 18, 19

Setting Up a Consecutive Setting Up a Consecutive Integer Word ProblemInteger Word Problem

There are 3 consecutive integers There are 3 consecutive integers whose sum is 27. Find the whose sum is 27. Find the integers.integers.

VariablesVariables

If n = the first consecutive integer then If n = the first consecutive integer then what is the second consecutive what is the second consecutive integer?integer?

Example)Example)

11 2 2 3 3

nn n+1 n+1 n+2 n+2

n = first consecutive integern = first consecutive integer

n+1 = second consecutive integern+1 = second consecutive integer

n+2 = third consecutive integern+2 = third consecutive integer

+1 +2

EquationEquation

There are 3 consecutive integers There are 3 consecutive integers whose sum is 27. Find the whose sum is 27. Find the integers.integers.

n + (n+1) + (n+2) = 27 n + (n+1) + (n+2) = 27

11stst 22ndnd 3 3rdrd

AnswerAnswer

The consecutive numbers are The consecutive numbers are

8, 9, 108, 9, 10

Your TurnYour Turn

There are 3 consecutive integers There are 3 consecutive integers whose sum is 333. Find the whose sum is 333. Find the integers.integers.

SolutionSolutionn = first consecutive integern = first consecutive integer

n+1 = second consecutive integern+1 = second consecutive integer

n+2 = third consecutive integern+2 = third consecutive integer

firstfirst + + secondsecond + + thirdthird = 333 = 333

Solution ContinuedSolution Continued

n = 110 n = 110 n+1 = 111n+1 = 111n+2 = 112n+2 = 112CheckCheck110 + 111 + 112 = 333110 + 111 + 112 = 333221 + 112 = 333221 + 112 = 333333 = 333333 = 333The three consecutive integers are The three consecutive integers are

110, 111, and 112110, 111, and 112

Consecutive Even/Odd Consecutive Even/Odd Integer ProblemsInteger Problems What if you wanted to find What if you wanted to find

consecutive even or consecutive odd consecutive even or consecutive odd numbers?numbers?

ODDODD

11 3 3 55

nn n+2n+2 n+4n+4

EVENEVEN

22 4 4 66

nn n+2n+2 n+4n+4

+2 +4

+2 +4

PracticePractice

There are 2 consecutive odd There are 2 consecutive odd integers whose sum is 36. Find integers whose sum is 36. Find the integers.the integers.

Another TryAnother TryThere are three consecutive even There are three consecutive even

integers whose sum is 54. Find integers whose sum is 54. Find the integers.the integers.

n = the first even integern = the first even integer

n+2 = the second even integern+2 = the second even integer

n+4 = the third even integern+4 = the third even integer

SolutionSolution

n + (n+2) + (n+4) = 54n + (n+2) + (n+4) = 543n + 6 = 543n + 6 = 543n = 483n = 48n = 16n = 16n+2 = 18n+2 = 18n+4 = 20n+4 = 20CheckCheck16 + 18 + 20 = 5616 + 18 + 20 = 5656 = 5656 = 56The 3 consecutive even integers are 16, 18 The 3 consecutive even integers are 16, 18

and 20.and 20.